Abstract
For a heuristic approach of the boundary variation in shape optimization, applicable for a special class of domains, the computation of second derivatives of domain and boundary integral functional are discussed. Moreover, for this approach the functional are Préchet-differentiable, because an embedding into a Banach space problem is possible. This implies symmetry and allows the discussion of sufficient condition in terms of a coercivity assumption on the second Fréchet-derivative. The theory is illustrated by a discussion of the Dido problem.
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Eppler, K. (1999). Fréchet-Differentiability and Sufficient Optimality Conditions for Shape Functionals. In: Hoffmann, KH., Leugering, G., Tröltzsch, F., Caesar, S. (eds) Optimal Control of Partial Differential Equations. ISNM International Series of Numerical Mathematics, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8691-8_11
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DOI: https://doi.org/10.1007/978-3-0348-8691-8_11
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9731-0
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